Alain Leroy worked with an engineering firm and an oil and gas company before heading the engineering subsidiary of an insurance group. He created and managed his own consulting company (Fractal Système) up until 2015.

• Preface xvChapter 1. Basic Concepts 11.1. Introduction 11.2. Definition of terms 11.2.1. Risk 11.2.2. Time definitions 21.2.3. Failures and repairs 41.2.4. IEC 61508 terms 81.3. Definition of parameters 101.3.1. Reliability 101.3.2. Maintainability 121.3.3. Availability and production availability 121.3.4. Dependability 131.3.5. Definitions used by maintenance engineers 131.3.6. Definitions used in the refinery industry 141.4. The exponential law/the constant failure rate 141.4.1. Reliability 141.4.2. Validity 151.4.3. Oil and gas industry 161.5. The bathtub curve 161.5.1. Meaning 161.5.2. Useful life and mission life 181.5.3. Validity 181.5.4. Oil and gas industry 18Chapter 2. Mathematics for Reliability 212.1. Introduction 212.2. Basis of probability and statistics 222.2.1. Boolean algebra 222.2.2. Probability relations 222.2.3. Probability distributions 242.2.4. Characteristics of probability distributions 242.2.5. Families and conjugates 262.3. Formulae and theorems 272.3.1. Combinatorial analysis 272.3.2. Central limit theorem 282.3.3. Chebyshev’s inequality 282.3.4. Laws of large numbers 282.3.5. Supporting functions and distributions 292.3.6. Bayes’ theorem 302.4. Useful discrete probability distributions 322.4.1. Binomial distribution 332.4.2. Poisson distribution. 332.5. Useful continuous probability distributions 352.5.1. Exponential distribution 352.5.2. Uniform distribution 362.5.3. Triangular distribution 372.5.4. Normal distribution 382.5.5. Log-normal distribution 402.5.6. Weibull distribution 432.5.7. Gamma distribution 442.5.8. Beta distribution 452.5.9. Chi-squared distribution 462.5.10. Fisher-Snedecor distribution 462.6. Statistical estimates 472.6.1. Estimates 472.6.2. Calculation of point estimate 472.6.3. Calculation of confidence interval 502.6.4. Heterogeneous samples 522.6.5. Implementation 532.7. Fitting of failure distribution 532.7.1. Principle 532.7.2. Median rank method 542.7.3. Implementation 552.8. Hypothesis testing 572.8.1. Principle 572.8.2. Existing tests. 582.8.3. Implementation 582.9. Bayesian reliability 602.9.1. Definition 602.9.2. Use of Bayes’ theorem 612.9.3. Bayesian inference 612.9.4. Selection of the prior probability distribution 622.9.5. Determination of the posterior probability distribution 622.9.6. Bayesian credibility interval 642.10. Extreme value probability distributions 652.10.1. Meaning. 652.10.2. The three extreme value probability distributions 652.10.3. Use in the industry 66Chapter 3. Assessment of Standard Systems 673.1. Introduction 673.2. Single item 673.2.1. Availability 683.2.2. Number of failures 693.3. System reliability 703.3.1. Series systems 703.3.2. Parallel systems 723.4. Specific architectures 733.4.1. Method of analysis 733.4.2. Redundant item system 743.5. On-guard items 763.5.1. Unrevealed failures 763.5.2. Full formula 773.5.3. Optimum proof test duration 79Chapter 4. Classic Methods 814.1. Introduction 814.2. Failure Mode and Effects Analysis 814.2.1. Conventional Failure Mode and Effects Analysis/Failure Mode,Effects and Criticality Analysis 814.2.2. Functional/hardware FMEA 844.2.3. Case study 844.3. Fault trees 894.3.1. Conventional fault trees 894.3.2. Fault tree extensions 934.3.3. Facilities provided by software packages 944.3.4. Case study 944.4. Reliability block diagrams 984.4.1. Conventional RBDs 984.4.2. RBD extension 1024.4.3. Facilities provided by software packages 1034.4.4. Case study 1034.5. Monte Carlo method 1044.5.1. Principle 1044.5.2. Use for production availability and reliability 1064.5.3. How many runs are enough? 107Chapter 5. Petri Net Method 1095.1. Introduction 1095.2. Petri nets 1105.2.1. Definition 1105.2.2. Mathematical properties 1115.2.3. Petri net construction 1125.2.4. GRAFCET 1175.3. IEC 62551 extensions 1175.3.1. Extensions to structure 1175.3.2. Modified execution rules 1205.4. Additional extensions 1215.4.1. Extensions to structure 1215.4.2. Modified execution rules 1225.5. Facilities provided by software packages 1235.5.1. Additional extensions to structure 1235.5.2. Modified execution rules 1235.5.3. Petri net processing 1235.5.4. Results 1235.6. Petri net construction 1245.6.1. Petri net modeling 1245.6.2. Minimizing the risk of error input 1245.6.3. Petri net checking 1245.6.4. Petri net validation 1255.7. Case study 1255.7.1. System description 1255.7.2. Petri net model 126Chapter 6. Sources of Reliability Data 1336.1. Introduction 1336.2. The OREDA project 1336.2.1. History 1336.2.2. Project management and organization 1356.2.3. Description of OREDA 2015 handbooks 1356.2.4. Use of the data tables 1376.2.5. Use of the additional tables 1416.2.6. Reliability database and data analysis software 1436.2.7. Data collection software 1446.3. The PDS handbook 1446.3.1. History 1446.3.2. Description of the handbook 1456.3.3. Use of the handbook 1456.4. Reliability Analysis Center/Reliability Information Analysis Center publications 1456.4.1. History 1456.4.2. Non-electronic Part Reliability Data handbook 1466.4.3. FMD 1466.4.4. NONOP 1466.4.5. Use of the publications 1466.5. Other publications 1476.5.1. EXIDA handbooks 1476.5.2. Electrical items 1476.5.3. Pipelines 1486.5.4. Flexibles 1496.5.5. Miscellaneous 1496.6. Missing information 150Chapter 7. Use of Reliability Test and Field Data 1517.1. Introduction 1517.2. Reliability test data 1517.2.1. Principle 1517.2.2. Test organization 1527.2.3. Assessment of failure rate 1527.3. Field data 1547.3.1. Principle 1547.3.2. Data collection organization 1557.3.3. Assessment of failure rate 1557.3.4. Assessment of probability to fail upon demand 1567.3.5. Assessment of MRT 1567.3.6. Case study 1567.4. Accelerated tests 1577.4.1. Principle 1577.4.2. Example 1587.4.3. Highly accelerated tests 1597.5. Reliability growth 1597.5.1. Principle 1597.5.2. Main models 159Chapter 8. Use of Expert Judgment. 1638.1. Introduction 1638.2. Basis 1648.2.1. Definitions 1648.2.2. Protocol for expert elicitation 1648.2.3. Role of the facilitator 1658.3. Characteristics of the experts 1668.3.1. Definition 1668.3.2. Selection 1668.3.3. Biases 1678.3.4. Expert weighting 1688.3.5. Expert dependence 1698.3.6. Aggregation of judgments 1698.4. Use of questionnaires 1698.4.1. Conditions of use 1698.4.2. The Delphi method 1708.4.3. Case study 1718.5. Use of interactive group 1738.5.1. Number of experts 1738.5.2. Procedure. 1738.6. Use of individual interviews 1748.6.1. Conditions of use 1748.6.2. Case study 1748.7. Bayesian aggregation of judgment 1758.7.1. Form of information provided by experts 1758.7.2. Assessment of failure rate (or MTBF) 1768.7.3. Assessment of probability of failure upon demand 1778.8. Validity of expert judgment 177Chapter 9. Supporting Topics 1799.1. Introduction 1799.2. Common cause failures 1799.2.1. Introduction 1799.2.2. Definition 1809.2.3. Defenses against CCF 1819.2.4. CCF modeling with the beta-factor method 1829.2.5. CCF modeling with the shock method 1859.2.6. Extension of the beta-factor model: the PDS method 1889.2.7. Field data 1899.2.8. Impact of CCF on system reliability 1909.2.9. Impact of testing policy on CCF 1919.2.10. Impact of CCF on system production availability 1949.2.11. Benchmark on CCF assessment 1949.3. Mechanical reliability 1959.3.1. Characteristics 1959.3.2. Stress-strength interference 1959.3.3. Empirical reliability relationships 1979.3.4. Comparison with system (constant failure rate) approach 1999.4. Reliability of electronic items 1999.4.1. Characteristics 1999.4.2. MIL-HDBK-217 2009.4.3. UTE-C-80811 2019.4.4. Other reliability data books 2019.4.5. EPRD 2039.4.6. Effect of dormancy period 2039.4.7. Common cause failures 2039.4.8. Comparison of previsions 2049.4.9. Use in the oil and gas industry 2059.5. Human reliability 2059.5.1. Human factors 2059.5.2. Human reliability in the nuclear industry 2059.5.3. Evaluation of HRA techniques 2069.5.4. Human reliability in the oil and gas industry 206Chapter 10. System Reliability Assessment 20910.1. Introduction 20910.2. Definition of reliability target 20910.2.1. Absolute reliability target 20910.2.2. Risk target 21010.3. Methodology of system reliability study 21110.3.1. Overall description 21110.3.2. Step 1: system analysis 21210.3.3. Step 2: qualitative analysis. 21210.3.4. Step 3: quantitative data selection 21210.3.5. Step 4: system reliability modeling 21410.3.6. Step 5: synthesis 21410.4. SIL studies 21410.4.1. Introduction 21410.4.2. SIL assignment 21410.4.3. SIL demonstration 21710.5. Description of the case study 21710.5.1. Origin of the risk 21710.5.2. Description of the standard SIF 21910.5.3. Risk assessment 21910.6. System analysis 22010.6.1. Description of HIPS functioning 22010.7. Qualitative analysis 22110.7.1. FMEA 22110.7.2. CCF analysis 22310.8. Quantitative data selection 22510.8.1. Selection of reliability data 22510.8.2. Collection of proof test data 22510.8.3. CCF quantification 22610.9. System reliability modeling 22610.9.1. Building of system reliability model 22610.9.2. System reliability calculation 22610.10. Synthesis 23210.10.1. Conclusions 23210.10.2. Recommendations 23310.11. Validity of system reliability assessments 23410.11.1. Reports 23410.11.2. Conclusions 234Chapter 11. Production Availability Assessment 23511.1. Introduction 23511.2. Definition of production availability target 23511.2.1. Absolute production availability target 23511.2.2. Economic target 23511.3. Methodology 23611.3.1. Events considered in production availability assessments 23611.3.2. Overall description 23611.3.3. Step 1: system analysis 23811.3.4. Step 2: quantitative data selection 23811.3.5. Step 3: production availability assessment 23811.3.6. Step 4: synthesis 23811.4. System analysis 23911.4.1. Determination of system running modes 23911.4.2. Item failure analysis 24211.5. Quantitative data selection 24411.5.1. Selection of reliability data 24411.5.2. Collection of operational data 24511.6. Production availability assessment 24611.6.1. Building of production availability model 24611.6.2. Production availability calculations 24611.7. Synthesis 24811.7.1. Main results 24811.7.2. Additional economic parameters 24911.7.3. Flared gas 25111.7.4. Other results 25311.7.5. Recommendations 25611.8. Uncertainty on the reliability parameters 25611.9. Validity of production availability assessments 257Chapter 12. Management of ProductionAvailability and Reliability 25912.1. Introduction 25912.2. Principles of dependability management 26012.2.1. Dependability property management 26012.2.2. Phasing of the management 26012.2.3. Lifecycle costing and dependability 26112.3. Technical specifications 26212.3.1. Contents. 26212.3.2. Reliability specification 26212.3.3. Production availability specification 26312.4. Reliability and production availability program 26412.4.1. Contents. 26412.4.2. Reliability program 26612.4.3. Production availability program 26712.5. Validation of system reliability 26712.5.1. Reliability data collection 26712.5.2. Random failures 26812.5.3. Common cause failures 26812.6. Validation of production availability 26812.6.1. Useful life 26812.6.2. Reliability data 26912.6.3. Production data 26912.6.4. Use of production availability model 269Appendices 271Appendix 1. Notations and Abbreviations 273Appendix 2. Markov Chain 283Appendix 3. Comparison of Modeling Methods 293Appendix 4. Solutions of Exercises. 301Bibliography 315Index 323

Alain Leroy worked with an engineering firm and an oil and gas company before heading the engineering subsidiary of an insurance group. He created and managed his own consulting company (Fractal Système) up until 2015.

• Preface xvChapter 1. Basic Concepts 11.1. Introduction 11.2. Definition of terms 11.2.1. Risk 11.2.2. Time definitions 21.2.3. Failures and repairs 41.2.4. IEC 61508 terms 81.3. Definition of parameters 101.3.1. Reliability 101.3.2. Maintainability 121.3.3. Availability and production availability 121.3.4. Dependability 131.3.5. Definitions used by maintenance engineers 131.3.6. Definitions used in the refinery industry 141.4. The exponential law/the constant failure rate 141.4.1. Reliability 141.4.2. Validity 151.4.3. Oil and gas industry 161.5. The bathtub curve 161.5.1. Meaning 161.5.2. Useful life and mission life 181.5.3. Validity 181.5.4. Oil and gas industry 18Chapter 2. Mathematics for Reliability 212.1. Introduction 212.2. Basis of probability and statistics 222.2.1. Boolean algebra 222.2.2. Probability relations 222.2.3. Probability distributions 242.2.4. Characteristics of probability distributions 242.2.5. Families and conjugates 262.3. Formulae and theorems 272.3.1. Combinatorial analysis 272.3.2. Central limit theorem 282.3.3. Chebyshev’s inequality 282.3.4. Laws of large numbers 282.3.5. Supporting functions and distributions 292.3.6. Bayes’ theorem 302.4. Useful discrete probability distributions 322.4.1. Binomial distribution 332.4.2. Poisson distribution. 332.5. Useful continuous probability distributions 352.5.1. Exponential distribution 352.5.2. Uniform distribution 362.5.3. Triangular distribution 372.5.4. Normal distribution 382.5.5. Log-normal distribution 402.5.6. Weibull distribution 432.5.7. Gamma distribution 442.5.8. Beta distribution 452.5.9. Chi-squared distribution 462.5.10. Fisher-Snedecor distribution 462.6. Statistical estimates 472.6.1. Estimates 472.6.2. Calculation of point estimate 472.6.3. Calculation of confidence interval 502.6.4. Heterogeneous samples 522.6.5. Implementation 532.7. Fitting of failure distribution 532.7.1. Principle 532.7.2. Median rank method 542.7.3. Implementation 552.8. Hypothesis testing 572.8.1. Principle 572.8.2. Existing tests. 582.8.3. Implementation 582.9. Bayesian reliability 602.9.1. Definition 602.9.2. Use of Bayes’ theorem 612.9.3. Bayesian inference 612.9.4. Selection of the prior probability distribution 622.9.5. Determination of the posterior probability distribution 622.9.6. Bayesian credibility interval 642.10. Extreme value probability distributions 652.10.1. Meaning. 652.10.2. The three extreme value probability distributions 652.10.3. Use in the industry 66Chapter 3. Assessment of Standard Systems 673.1. Introduction 673.2. Single item 673.2.1. Availability 683.2.2. Number of failures 693.3. System reliability 703.3.1. Series systems 703.3.2. Parallel systems 723.4. Specific architectures 733.4.1. Method of analysis 733.4.2. Redundant item system 743.5. On-guard items 763.5.1. Unrevealed failures 763.5.2. Full formula 773.5.3. Optimum proof test duration 79Chapter 4. Classic Methods 814.1. Introduction 814.2. Failure Mode and Effects Analysis 814.2.1. Conventional Failure Mode and Effects Analysis/Failure Mode,Effects and Criticality Analysis 814.2.2. Functional/hardware FMEA 844.2.3. Case study 844.3. Fault trees 894.3.1. Conventional fault trees 894.3.2. Fault tree extensions 934.3.3. Facilities provided by software packages 944.3.4. Case study 944.4. Reliability block diagrams 984.4.1. Conventional RBDs 984.4.2. RBD extension 1024.4.3. Facilities provided by software packages 1034.4.4. Case study 1034.5. Monte Carlo method 1044.5.1. Principle 1044.5.2. Use for production availability and reliability 1064.5.3. How many runs are enough? 107Chapter 5. Petri Net Method 1095.1. Introduction 1095.2. Petri nets 1105.2.1. Definition 1105.2.2. Mathematical properties 1115.2.3. Petri net construction 1125.2.4. GRAFCET 1175.3. IEC 62551 extensions 1175.3.1. Extensions to structure 1175.3.2. Modified execution rules 1205.4. Additional extensions 1215.4.1. Extensions to structure 1215.4.2. Modified execution rules 1225.5. Facilities provided by software packages 1235.5.1. Additional extensions to structure 1235.5.2. Modified execution rules 1235.5.3. Petri net processing 1235.5.4. Results 1235.6. Petri net construction 1245.6.1. Petri net modeling 1245.6.2. Minimizing the risk of error input 1245.6.3. Petri net checking 1245.6.4. Petri net validation 1255.7. Case study 1255.7.1. System description 1255.7.2. Petri net model 126Chapter 6. Sources of Reliability Data 1336.1. Introduction 1336.2. The OREDA project 1336.2.1. History 1336.2.2. Project management and organization 1356.2.3. Description of OREDA 2015 handbooks 1356.2.4. Use of the data tables 1376.2.5. Use of the additional tables 1416.2.6. Reliability database and data analysis software 1436.2.7. Data collection software 1446.3. The PDS handbook 1446.3.1. History 1446.3.2. Description of the handbook 1456.3.3. Use of the handbook 1456.4. Reliability Analysis Center/Reliability Information Analysis Center publications 1456.4.1. History 1456.4.2. Non-electronic Part Reliability Data handbook 1466.4.3. FMD 1466.4.4. NONOP 1466.4.5. Use of the publications 1466.5. Other publications 1476.5.1. EXIDA handbooks 1476.5.2. Electrical items 1476.5.3. Pipelines 1486.5.4. Flexibles 1496.5.5. Miscellaneous 1496.6. Missing information 150Chapter 7. Use of Reliability Test and Field Data 1517.1. Introduction 1517.2. Reliability test data 1517.2.1. Principle 1517.2.2. Test organization 1527.2.3. Assessment of failure rate 1527.3. Field data 1547.3.1. Principle 1547.3.2. Data collection organization 1557.3.3. Assessment of failure rate 1557.3.4. Assessment of probability to fail upon demand 1567.3.5. Assessment of MRT 1567.3.6. Case study 1567.4. Accelerated tests 1577.4.1. Principle 1577.4.2. Example 1587.4.3. Highly accelerated tests 1597.5. Reliability growth 1597.5.1. Principle 1597.5.2. Main models 159Chapter 8. Use of Expert Judgment. 1638.1. Introduction 1638.2. Basis 1648.2.1. Definitions 1648.2.2. Protocol for expert elicitation 1648.2.3. Role of the facilitator 1658.3. Characteristics of the experts 1668.3.1. Definition 1668.3.2. Selection 1668.3.3. Biases 1678.3.4. Expert weighting 1688.3.5. Expert dependence 1698.3.6. Aggregation of judgments 1698.4. Use of questionnaires 1698.4.1. Conditions of use 1698.4.2. The Delphi method 1708.4.3. Case study 1718.5. Use of interactive group 1738.5.1. Number of experts 1738.5.2. Procedure. 1738.6. Use of individual interviews 1748.6.1. Conditions of use 1748.6.2. Case study 1748.7. Bayesian aggregation of judgment 1758.7.1. Form of information provided by experts 1758.7.2. Assessment of failure rate (or MTBF) 1768.7.3. Assessment of probability of failure upon demand 1778.8. Validity of expert judgment 177Chapter 9. Supporting Topics 1799.1. Introduction 1799.2. Common cause failures 1799.2.1. Introduction 1799.2.2. Definition 1809.2.3. Defenses against CCF 1819.2.4. CCF modeling with the beta-factor method 1829.2.5. CCF modeling with the shock method 1859.2.6. Extension of the beta-factor model: the PDS method 1889.2.7. Field data 1899.2.8. Impact of CCF on system reliability 1909.2.9. Impact of testing policy on CCF 1919.2.10. Impact of CCF on system production availability 1949.2.11. Benchmark on CCF assessment 1949.3. Mechanical reliability 1959.3.1. Characteristics 1959.3.2. Stress-strength interference 1959.3.3. Empirical reliability relationships 1979.3.4. Comparison with system (constant failure rate) approach 1999.4. Reliability of electronic items 1999.4.1. Characteristics 1999.4.2. MIL-HDBK-217 2009.4.3. UTE-C-80811 2019.4.4. Other reliability data books 2019.4.5. EPRD 2039.4.6. Effect of dormancy period 2039.4.7. Common cause failures 2039.4.8. Comparison of previsions 2049.4.9. Use in the oil and gas industry 2059.5. Human reliability 2059.5.1. Human factors 2059.5.2. Human reliability in the nuclear industry 2059.5.3. Evaluation of HRA techniques 2069.5.4. Human reliability in the oil and gas industry 206Chapter 10. System Reliability Assessment 20910.1. Introduction 20910.2. Definition of reliability target 20910.2.1. Absolute reliability target 20910.2.2. Risk target 21010.3. Methodology of system reliability study 21110.3.1. Overall description 21110.3.2. Step 1: system analysis 21210.3.3. Step 2: qualitative analysis. 21210.3.4. Step 3: quantitative data selection 21210.3.5. Step 4: system reliability modeling 21410.3.6. Step 5: synthesis 21410.4. SIL studies 21410.4.1. Introduction 21410.4.2. SIL assignment 21410.4.3. SIL demonstration 21710.5. Description of the case study 21710.5.1. Origin of the risk 21710.5.2. Description of the standard SIF 21910.5.3. Risk assessment 21910.6. System analysis 22010.6.1. Description of HIPS functioning 22010.7. Qualitative analysis 22110.7.1. FMEA 22110.7.2. CCF analysis 22310.8. Quantitative data selection 22510.8.1. Selection of reliability data 22510.8.2. Collection of proof test data 22510.8.3. CCF quantification 22610.9. System reliability modeling 22610.9.1. Building of system reliability model 22610.9.2. System reliability calculation 22610.10. Synthesis 23210.10.1. Conclusions 23210.10.2. Recommendations 23310.11. Validity of system reliability assessments 23410.11.1. Reports 23410.11.2. Conclusions 234Chapter 11. Production Availability Assessment 23511.1. Introduction 23511.2. Definition of production availability target 23511.2.1. Absolute production availability target 23511.2.2. Economic target 23511.3. Methodology 23611.3.1. Events considered in production availability assessments 23611.3.2. Overall description 23611.3.3. Step 1: system analysis 23811.3.4. Step 2: quantitative data selection 23811.3.5. Step 3: production availability assessment 23811.3.6. Step 4: synthesis 23811.4. System analysis 23911.4.1. Determination of system running modes 23911.4.2. Item failure analysis 24211.5. Quantitative data selection 24411.5.1. Selection of reliability data 24411.5.2. Collection of operational data 24511.6. Production availability assessment 24611.6.1. Building of production availability model 24611.6.2. Production availability calculations 24611.7. Synthesis 24811.7.1. Main results 24811.7.2. Additional economic parameters 24911.7.3. Flared gas 25111.7.4. Other results 25311.7.5. Recommendations 25611.8. Uncertainty on the reliability parameters 25611.9. Validity of production availability assessments 257Chapter 12. Management of ProductionAvailability and Reliability 25912.1. Introduction 25912.2. Principles of dependability management 26012.2.1. Dependability property management 26012.2.2. Phasing of the management 26012.2.3. Lifecycle costing and dependability 26112.3. Technical specifications 26212.3.1. Contents. 26212.3.2. Reliability specification 26212.3.3. Production availability specification 26312.4. Reliability and production availability program 26412.4.1. Contents. 26412.4.2. Reliability program 26612.4.3. Production availability program 26712.5. Validation of system reliability 26712.5.1. Reliability data collection 26712.5.2. Random failures 26812.5.3. Common cause failures 26812.6. Validation of production availability 26812.6.1. Useful life 26812.6.2. Reliability data 26912.6.3. Production data 26912.6.4. Use of production availability model 269Appendices 271Appendix 1. Notations and Abbreviations 273Appendix 2. Markov Chain 283Appendix 3. Comparison of Modeling Methods 293Appendix 4. Solutions of Exercises. 301Bibliography 315Index 323

Alain Leroy worked with an engineering firm and an oil and gas company before heading the engineering subsidiary of an insurance group. He created and managed his own consulting company (Fractal Système) up until 2015.

• Preface xvChapter 1. Basic Concepts 11.1. Introduction 11.2. Definition of terms 11.2.1. Risk 11.2.2. Time definitions 21.2.3. Failures and repairs 41.2.4. IEC 61508 terms 81.3. Definition of parameters 101.3.1. Reliability 101.3.2. Maintainability 121.3.3. Availability and production availability 121.3.4. Dependability 131.3.5. Definitions used by maintenance engineers 131.3.6. Definitions used in the refinery industry 141.4. The exponential law/the constant failure rate 141.4.1. Reliability 141.4.2. Validity 151.4.3. Oil and gas industry 161.5. The bathtub curve 161.5.1. Meaning 161.5.2. Useful life and mission life 181.5.3. Validity 181.5.4. Oil and gas industry 18Chapter 2. Mathematics for Reliability 212.1. Introduction 212.2. Basis of probability and statistics 222.2.1. Boolean algebra 222.2.2. Probability relations 222.2.3. Probability distributions 242.2.4. Characteristics of probability distributions 242.2.5. Families and conjugates 262.3. Formulae and theorems 272.3.1. Combinatorial analysis 272.3.2. Central limit theorem 282.3.3. Chebyshev’s inequality 282.3.4. Laws of large numbers 282.3.5. Supporting functions and distributions 292.3.6. Bayes’ theorem 302.4. Useful discrete probability distributions 322.4.1. Binomial distribution 332.4.2. Poisson distribution. 332.5. Useful continuous probability distributions 352.5.1. Exponential distribution 352.5.2. Uniform distribution 362.5.3. Triangular distribution 372.5.4. Normal distribution 382.5.5. Log-normal distribution 402.5.6. Weibull distribution 432.5.7. Gamma distribution 442.5.8. Beta distribution 452.5.9. Chi-squared distribution 462.5.10. Fisher-Snedecor distribution 462.6. Statistical estimates 472.6.1. Estimates 472.6.2. Calculation of point estimate 472.6.3. Calculation of confidence interval 502.6.4. Heterogeneous samples 522.6.5. Implementation 532.7. Fitting of failure distribution 532.7.1. Principle 532.7.2. Median rank method 542.7.3. Implementation 552.8. Hypothesis testing 572.8.1. Principle 572.8.2. Existing tests. 582.8.3. Implementation 582.9. Bayesian reliability 602.9.1. Definition 602.9.2. Use of Bayes’ theorem 612.9.3. Bayesian inference 612.9.4. Selection of the prior probability distribution 622.9.5. Determination of the posterior probability distribution 622.9.6. Bayesian credibility interval 642.10. Extreme value probability distributions 652.10.1. Meaning. 652.10.2. The three extreme value probability distributions 652.10.3. Use in the industry 66Chapter 3. Assessment of Standard Systems 673.1. Introduction 673.2. Single item 673.2.1. Availability 683.2.2. Number of failures 693.3. System reliability 703.3.1. Series systems 703.3.2. Parallel systems 723.4. Specific architectures 733.4.1. Method of analysis 733.4.2. Redundant item system 743.5. On-guard items 763.5.1. Unrevealed failures 763.5.2. Full formula 773.5.3. Optimum proof test duration 79Chapter 4. Classic Methods 814.1. Introduction 814.2. Failure Mode and Effects Analysis 814.2.1. Conventional Failure Mode and Effects Analysis/Failure Mode,Effects and Criticality Analysis 814.2.2. Functional/hardware FMEA 844.2.3. Case study 844.3. Fault trees 894.3.1. Conventional fault trees 894.3.2. Fault tree extensions 934.3.3. Facilities provided by software packages 944.3.4. Case study 944.4. Reliability block diagrams 984.4.1. Conventional RBDs 984.4.2. RBD extension 1024.4.3. Facilities provided by software packages 1034.4.4. Case study 1034.5. Monte Carlo method 1044.5.1. Principle 1044.5.2. Use for production availability and reliability 1064.5.3. How many runs are enough? 107Chapter 5. Petri Net Method 1095.1. Introduction 1095.2. Petri nets 1105.2.1. Definition 1105.2.2. Mathematical properties 1115.2.3. Petri net construction 1125.2.4. GRAFCET 1175.3. IEC 62551 extensions 1175.3.1. Extensions to structure 1175.3.2. Modified execution rules 1205.4. Additional extensions 1215.4.1. Extensions to structure 1215.4.2. Modified execution rules 1225.5. Facilities provided by software packages 1235.5.1. Additional extensions to structure 1235.5.2. Modified execution rules 1235.5.3. Petri net processing 1235.5.4. Results 1235.6. Petri net construction 1245.6.1. Petri net modeling 1245.6.2. Minimizing the risk of error input 1245.6.3. Petri net checking 1245.6.4. Petri net validation 1255.7. Case study 1255.7.1. System description 1255.7.2. Petri net model 126Chapter 6. Sources of Reliability Data 1336.1. Introduction 1336.2. The OREDA project 1336.2.1. History 1336.2.2. Project management and organization 1356.2.3. Description of OREDA 2015 handbooks 1356.2.4. Use of the data tables 1376.2.5. Use of the additional tables 1416.2.6. Reliability database and data analysis software 1436.2.7. Data collection software 1446.3. The PDS handbook 1446.3.1. History 1446.3.2. Description of the handbook 1456.3.3. Use of the handbook 1456.4. Reliability Analysis Center/Reliability Information Analysis Center publications 1456.4.1. History 1456.4.2. Non-electronic Part Reliability Data handbook 1466.4.3. FMD 1466.4.4. NONOP 1466.4.5. Use of the publications 1466.5. Other publications 1476.5.1. EXIDA handbooks 1476.5.2. Electrical items 1476.5.3. Pipelines 1486.5.4. Flexibles 1496.5.5. Miscellaneous 1496.6. Missing information 150Chapter 7. Use of Reliability Test and Field Data 1517.1. Introduction 1517.2. Reliability test data 1517.2.1. Principle 1517.2.2. Test organization 1527.2.3. Assessment of failure rate 1527.3. Field data 1547.3.1. Principle 1547.3.2. Data collection organization 1557.3.3. Assessment of failure rate 1557.3.4. Assessment of probability to fail upon demand 1567.3.5. Assessment of MRT 1567.3.6. Case study 1567.4. Accelerated tests 1577.4.1. Principle 1577.4.2. Example 1587.4.3. Highly accelerated tests 1597.5. Reliability growth 1597.5.1. Principle 1597.5.2. Main models 159Chapter 8. Use of Expert Judgment. 1638.1. Introduction 1638.2. Basis 1648.2.1. Definitions 1648.2.2. Protocol for expert elicitation 1648.2.3. Role of the facilitator 1658.3. Characteristics of the experts 1668.3.1. Definition 1668.3.2. Selection 1668.3.3. Biases 1678.3.4. Expert weighting 1688.3.5. Expert dependence 1698.3.6. Aggregation of judgments 1698.4. Use of questionnaires 1698.4.1. Conditions of use 1698.4.2. The Delphi method 1708.4.3. Case study 1718.5. Use of interactive group 1738.5.1. Number of experts 1738.5.2. Procedure. 1738.6. Use of individual interviews 1748.6.1. Conditions of use 1748.6.2. Case study 1748.7. Bayesian aggregation of judgment 1758.7.1. Form of information provided by experts 1758.7.2. Assessment of failure rate (or MTBF) 1768.7.3. Assessment of probability of failure upon demand 1778.8. Validity of expert judgment 177Chapter 9. Supporting Topics 1799.1. Introduction 1799.2. Common cause failures 1799.2.1. Introduction 1799.2.2. Definition 1809.2.3. Defenses against CCF 1819.2.4. CCF modeling with the beta-factor method 1829.2.5. CCF modeling with the shock method 1859.2.6. Extension of the beta-factor model: the PDS method 1889.2.7. Field data 1899.2.8. Impact of CCF on system reliability 1909.2.9. Impact of testing policy on CCF 1919.2.10. Impact of CCF on system production availability 1949.2.11. Benchmark on CCF assessment 1949.3. Mechanical reliability 1959.3.1. Characteristics 1959.3.2. Stress-strength interference 1959.3.3. Empirical reliability relationships 1979.3.4. Comparison with system (constant failure rate) approach 1999.4. Reliability of electronic items 1999.4.1. Characteristics 1999.4.2. MIL-HDBK-217 2009.4.3. UTE-C-80811 2019.4.4. Other reliability data books 2019.4.5. EPRD 2039.4.6. Effect of dormancy period 2039.4.7. Common cause failures 2039.4.8. Comparison of previsions 2049.4.9. Use in the oil and gas industry 2059.5. Human reliability 2059.5.1. Human factors 2059.5.2. Human reliability in the nuclear industry 2059.5.3. Evaluation of HRA techniques 2069.5.4. Human reliability in the oil and gas industry 206Chapter 10. System Reliability Assessment 20910.1. Introduction 20910.2. Definition of reliability target 20910.2.1. Absolute reliability target 20910.2.2. Risk target 21010.3. Methodology of system reliability study 21110.3.1. Overall description 21110.3.2. Step 1: system analysis 21210.3.3. Step 2: qualitative analysis. 21210.3.4. Step 3: quantitative data selection 21210.3.5. Step 4: system reliability modeling 21410.3.6. Step 5: synthesis 21410.4. SIL studies 21410.4.1. Introduction 21410.4.2. SIL assignment 21410.4.3. SIL demonstration 21710.5. Description of the case study 21710.5.1. Origin of the risk 21710.5.2. Description of the standard SIF 21910.5.3. Risk assessment 21910.6. System analysis 22010.6.1. Description of HIPS functioning 22010.7. Qualitative analysis 22110.7.1. FMEA 22110.7.2. CCF analysis 22310.8. Quantitative data selection 22510.8.1. Selection of reliability data 22510.8.2. Collection of proof test data 22510.8.3. CCF quantification 22610.9. System reliability modeling 22610.9.1. Building of system reliability model 22610.9.2. System reliability calculation 22610.10. Synthesis 23210.10.1. Conclusions 23210.10.2. Recommendations 23310.11. Validity of system reliability assessments 23410.11.1. Reports 23410.11.2. Conclusions 234Chapter 11. Production Availability Assessment 23511.1. Introduction 23511.2. Definition of production availability target 23511.2.1. Absolute production availability target 23511.2.2. Economic target 23511.3. Methodology 23611.3.1. Events considered in production availability assessments 23611.3.2. Overall description 23611.3.3. Step 1: system analysis 23811.3.4. Step 2: quantitative data selection 23811.3.5. Step 3: production availability assessment 23811.3.6. Step 4: synthesis 23811.4. System analysis 23911.4.1. Determination of system running modes 23911.4.2. Item failure analysis 24211.5. Quantitative data selection 24411.5.1. Selection of reliability data 24411.5.2. Collection of operational data 24511.6. Production availability assessment 24611.6.1. Building of production availability model 24611.6.2. Production availability calculations 24611.7. Synthesis 24811.7.1. Main results 24811.7.2. Additional economic parameters 24911.7.3. Flared gas 25111.7.4. Other results 25311.7.5. Recommendations 25611.8. Uncertainty on the reliability parameters 25611.9. Validity of production availability assessments 257Chapter 12. Management of ProductionAvailability and Reliability 25912.1. Introduction 25912.2. Principles of dependability management 26012.2.1. Dependability property management 26012.2.2. Phasing of the management 26012.2.3. Lifecycle costing and dependability 26112.3. Technical specifications 26212.3.1. Contents. 26212.3.2. Reliability specification 26212.3.3. Production availability specification 26312.4. Reliability and production availability program 26412.4.1. Contents. 26412.4.2. Reliability program 26612.4.3. Production availability program 26712.5. Validation of system reliability 26712.5.1. Reliability data collection 26712.5.2. Random failures 26812.5.3. Common cause failures 26812.6. Validation of production availability 26812.6.1. Useful life 26812.6.2. Reliability data 26912.6.3. Production data 26912.6.4. Use of production availability model 269Appendices 271Appendix 1. Notations and Abbreviations 273Appendix 2. Markov Chain 283Appendix 3. Comparison of Modeling Methods 293Appendix 4. Solutions of Exercises. 301Bibliography 315Index 323